Factoring a four degree polynomial, newbie question

Thanks for this quick response, but how to use your method if we have more radicals, for example


a:sqrt(3); b:sqrt(2);
p:(a*x^2-3*y+b)*(y^2+b*y+a)$
p:expand(p);
p:ratsubst(q,sqrt(2),p);
p:ratsubst(r,sqrt(3),p);
 
Something like factor(p, q^2-2, r^2-3) don't work




________________________________
From: Stavros Macrakis <macrakis at alum.mit.edu>
To: gelu precup <geluprecup at yahoo.com>
Cc: maxima at math.utexas.edu
Sent: Thu, January 21, 2010 8:40:52 PM
Subject: Re: [Maxima] Factoring a four degree polynomial, newbie question

You need to express the sqrt(2) in your input in terms of q:

ratsubst(q,sqrt(2),p);
  =>   -3*y^3+(q*x^2+q-3)*y^2+(q*x^2-q^3)*y+2*x^2+2

factor(%,q^2-2)
  =>   -(3*y-q*x^2-q)*(y^2+y+q)

It is important to use ratsubst rather than subst here, otherwise (e.g.) 2^(3/2) is not recognized as q^3. Also, subst will substitute in the exponents, which you don't want.

             -s


On Thu, Jan 21, 2010 at 1:31 PM, gelu precup <geluprecup at yahoo.com> wrote:

-(3*y^3-sqrt(2)*x^2*y^2-sqrt(2)*y^2+3*y^2-sqrt(2)*x^2*y+2^(3/2)*y-2*x^2-2)